If you decide to use a PIC, you can either go with the PIC16 or PIC18 series.
PIC18:
This is the same product family as the one in the RC, so you can use the same development environment (MPLAB + mcc18, but not IFI loader). Most of these come in non-DIP packages or are too large for what you need, but given your requirements the PIC18F1220 will work.
PIC16:
These are generally smaller and less powerful than the PIC18, but still plenty powerful for your needs. The problem with PIC16 is there are no free fully featured C compilers for it (as far as I know), but there are some free limited ones you may be able to use. The assembler is free if you're insane. There are too many PIC16s that match your requirements, so use Microchip's product comparator to find the right one for you (get one with flash memory, ie 16F series, and at least one CCP for PWM). The PIC16F88 is a popular choice.
With any PIC you'll need to find a programmer (to actually get the code onto the processor). You can buy one from
microchip, but they can be pretty expensive. Or you can try to google some cheap versions you can build/buy (make sure to get the software you need too).
A good alternative to a PIC is an AVR. Unlike PICs, there is an
AVR gcc C/C++ compiler that comes with a great set of tools. You can compare AVRs
here, but I recommend the
ATtiny44. You'll also need a programmer for the AVRs. There are some
cheap ones, but you'll have to find one that works with a ATtiny.